@article {Fokas:2012:0022-2526:51,
title = "Generalized DirichlettoNeumann Map in TimeDependent Domains",
journal = "Studies in Applied Mathematics",
parent_itemid = "infobike://bpl/sapm",
publishercode ="bp",
year = "2012",
volume = "129",
number = "1",
publication date ="2012-07-01T00:00:00",
pages = "51-90",
itemtype = "ARTICLE",
issn = "0022-2526",
eissn = "1467-9590",
url = "https://www.ingentaconnect.com/content/bpl/sapm/2012/00000129/00000001/art00003",
doi = "doi:10.1111/j.1467-9590.2011.00545.x",
author = "Fokas, A. S. and Pelloni, B.",
abstract = "We study the heat, linear Schr{\"o}dinger (LS), and linear KdV equations in the domain l(t) x , 0 t T, with prescribed initial and boundary
conditions and with l(t) a given differentiable function. For the first two equations, we show that the unknown Neumann or Dirichlet boundary value can be computed as the solution of a linear Volterra integral equation with an explicit
weakly singular kernel. This integral equation can be derived from the formal Fourier integral representation of the solution. For the linear KdV equation we show that the two unknown boundary values can be computed as the solution of a system of linear Volterra integral equations with explicit
weakly singular kernels. The derivation in this case makes crucial use of analyticity and certain invariance properties in the complex spectral plane. The above Volterra equations are shown to admit a unique solution.",
}